broadband least-squares wave-equation migration - · pdf filebroadband least-squares...

of 5/5
Broadband Least-Squares Wave-Equation Migration Shaoping Lu*, Xiang Li, A.A. Valenciano, Nizar Chemingui (PGS) and Cheng Cheng (UC-Berkeley) Summary In general, Least-Squares Migration (LSM) can produce images corrected for overburden effects, variations in illumination, and incomplete acquisition geometry. The modeling engine of our LSM implementation consists of a visco-acoustic anisotropic one-way wave-equation extrapolator. It has the advantage of efficiently propagating high-frequency seismic data using high-resolution earth models (e.g. derived from Full Waveform Inversion). Applications to synthetic and field data examples (from the Gulf of Mexico and the North Sea) consistently delivered higher resolution images with better amplitude balance when compared to standard seismic migration. Introduction Depth migration produces a blurred representation of the earth reflectivity, with biased illumination and limited wavenumber content. The image resolution at a given depth is controlled by the migration operators, the acquisition parameters (source signature, frequency bandwidth, acquisition geometry), and the earth properties at the reflector depth and the overburden (velocity, attenuation). Some of these conditions can be mitigated during acquisition and processing by employing technologies like: multi-sensor data, full azimuth acquisition geometries, deghosting, attenuation compensation and using high- resolution earth models during depth migration (i.e. models derived from Full Waveform Inversion). However, when heterogeneities are present in the earth and the acquisition geometry leads to insufficient source and receiver coverage on the surface, both the illumination and wavenumber content of the depth-migrated images can be significantly restricted. The resolution of the depth images can be improved by posing the imaging problem in terms of least squares inversion. The Least-Squares Migration (LSM) solutions (Schuster, 1993; Nemeth et al., 1999; Prucha and Biondi, 2002) are designed to produce images of the subsurface corrected for wavefield distortions caused by acquisition and propagation effects. They implicitly solve for the earth reflectivity by means of data residual reduction in an iterative fashion, which usually demands intensive computation. In seismic exploration framework, Nemeth et al. (1999) derived a Least-Squares Migration following a high-frequency Kirchhoff integral asymptotic approximation (ray-based). Later, Prucha and Biondi (2002) derived less restrictive broadband wave equation solutions. The advantage of broadband wave-equation extrapolators is that they make better use of the high- resolution earth models derived with advanced processing technologies such as Full Waveform Inversion FWI (Korsmo et al., 2017). Here, we implement an LSM using an accurate visco- acoustic anisotropic one-way wave-equation operator (Valenciano et al., 2011). Our application integrates the one-way operator with a fast linear inversion solver in an efficient migration/demigration workflow, namely a Least- Squares one-way Wave-Equation Migration (LS-WEM). Applications of LS-WEM to both synthetic and field data examples improve images amplitude balance and enhance both temporal and spatial resolution. Methodology Seismic migration is the adjoint solution to the forward modeling problem: m = L T d obs (1) where, d obs is the observed data , L represents the linearized (Born) modeling operator, and its adjoint L T is the migration operator. However, the heterogeneity of the overburden and/or limitations of the acquisition geometry can affect the illumination and wavenumber content of the estimated image m. A better approximation of the earth reflectivity is obtained by using a least squares inversion, which solves a minimization problem to approximate the true reflectivity m as: m = argmin m || d obs Lm || 2 2 (2) In this case, the acquisition geometry, which relates to the operator L, has less effect to the resulting image m. Here we introduce an implicit method to solve the Least- Squares problem. The LSM simulates data by wave- equation Born modeling, and iteratively updates the reflectivity by migration of the misfits between the observed and simulated data. The algorithm can be summarized by the diagram in Figure 1 using an iterative modeling/migration framework. The first step of the flow is to produce an approximate reflectivity (migration). In the next step, the reflectivity is used in Born modeling. When the data residual || d obs - d mod || is large, it is migrated to update the image m. The inversion converges when the simulated data matches the observation. One iteration (blue loop in Figure 1) comprises one Born modeling and one migration. © 2017 SEG SEG International Exposition and 87th Annual Meeting Page 4422 Downloaded 09/15/17 to 217.144.243.100. Redistribution subject to SEG license or copyright; see Terms of Use at http://library.seg.org/

Post on 19-Mar-2018

214 views

Category:

Documents

1 download

Embed Size (px)

TRANSCRIPT

  • Broadband Least-Squares Wave-Equation Migration

    Shaoping Lu*, Xiang Li, A.A. Valenciano, Nizar Chemingui (PGS) and Cheng Cheng (UC-Berkeley)

    Summary

    In general, Least-Squares Migration (LSM) can produce

    images corrected for overburden effects, variations in

    illumination, and incomplete acquisition geometry. The

    modeling engine of our LSM implementation consists of a

    visco-acoustic anisotropic one-way wave-equation

    extrapolator. It has the advantage of efficiently propagating

    high-frequency seismic data using high-resolution earth

    models (e.g. derived from Full Waveform Inversion).

    Applications to synthetic and field data examples (from the

    Gulf of Mexico and the North Sea) consistently delivered

    higher resolution images with better amplitude balance

    when compared to standard seismic migration.

    Introduction

    Depth migration produces a blurred representation of the

    earth reflectivity, with biased illumination and limited

    wavenumber content. The image resolution at a given depth

    is controlled by the migration operators, the acquisition

    parameters (source signature, frequency bandwidth,

    acquisition geometry), and the earth properties at the

    reflector depth and the overburden (velocity, attenuation).

    Some of these conditions can be mitigated during

    acquisition and processing by employing technologies like:

    multi-sensor data, full azimuth acquisition geometries,

    deghosting, attenuation compensation and using high-

    resolution earth models during depth migration (i.e. models

    derived from Full Waveform Inversion). However, when

    heterogeneities are present in the earth and the acquisition

    geometry leads to insufficient source and receiver coverage

    on the surface, both the illumination and wavenumber

    content of the depth-migrated images can be significantly

    restricted.

    The resolution of the depth images can be improved by

    posing the imaging problem in terms of least squares

    inversion. The Least-Squares Migration (LSM) solutions

    (Schuster, 1993; Nemeth et al., 1999; Prucha and Biondi,

    2002) are designed to produce images of the subsurface

    corrected for wavefield distortions caused by acquisition

    and propagation effects. They implicitly solve for the earth

    reflectivity by means of data residual reduction in an

    iterative fashion, which usually demands intensive

    computation. In seismic exploration framework, Nemeth et

    al. (1999) derived a Least-Squares Migration following a

    high-frequency Kirchhoff integral asymptotic

    approximation (ray-based). Later, Prucha and Biondi

    (2002) derived less restrictive broadband wave equation

    solutions. The advantage of broadband wave-equation

    extrapolators is that they make better use of the high-

    resolution earth models derived with advanced processing

    technologies such as Full Waveform Inversion FWI

    (Korsmo et al., 2017).

    Here, we implement an LSM using an accurate visco-

    acoustic anisotropic one-way wave-equation operator

    (Valenciano et al., 2011). Our application integrates the

    one-way operator with a fast linear inversion solver in an

    efficient migration/demigration workflow, namely a Least-

    Squares one-way Wave-Equation Migration (LS-WEM).

    Applications of LS-WEM to both synthetic and field data

    examples improve images amplitude balance and enhance

    both temporal and spatial resolution.

    Methodology

    Seismic migration is the adjoint solution to the forward

    modeling problem:

    m = LT

    dobs (1)

    where, dobs is the observed data , L represents the linearized

    (Born) modeling operator, and its adjoint LT is the

    migration operator. However, the heterogeneity of the

    overburden and/or limitations of the acquisition geometry

    can affect the illumination and wavenumber content of the

    estimated image m.

    A better approximation of the earth reflectivity is obtained

    by using a least squares inversion, which solves a

    minimization problem to approximate the true reflectivity

    m as:

    m = argminm || dobs Lm ||2

    2 (2)

    In this case, the acquisition geometry, which relates to the

    operator L, has less effect to the resulting image m.

    Here we introduce an implicit method to solve the Least-

    Squares problem. The LSM simulates data by wave-

    equation Born modeling, and iteratively updates the

    reflectivity by migration of the misfits between the

    observed and simulated data. The algorithm can be

    summarized by the diagram in Figure 1 using an iterative

    modeling/migration framework. The first step of the flow is

    to produce an approximate reflectivity (migration). In the

    next step, the reflectivity is used in Born modeling. When

    the data residual || dobs - dmod || is large, it is migrated to

    update the image m. The inversion converges when the

    simulated data matches the observation. One iteration (blue

    loop in Figure 1) comprises one Born modeling and one

    migration.

    2017 SEG SEG International Exposition and 87th Annual Meeting

    Page 4422

    Dow

    nloa

    ded

    09/1

    5/17

    to 2

    17.1

    44.2

    43.1

    00. R

    edis

    trib

    utio

    n su

    bjec

    t to

    SEG

    lice

    nse

    or c

    opyr

    ight

    ; see

    Ter

    ms

    of U

    se a

    t http

    ://lib

    rary

    .seg

    .org

    /

  • Broadband Least-Squares Wave-Equation Migration

    The computational cost of the iterative LSM relies on the

    efficiency of the wavefield propagation algorithm. Here,

    we implement the inversion using a one-way wave-

    equation operator (Valenciano et al., 2011), which has

    advantages of both accuracy and efficiency. In addition, our

    implementation combines the one-way extrapolator with

    fast linear inversion solvers into an efficient migration

    inversion system.

    Synthetic and field data examples

    We have applied LS-WEM to the 2D Sigsbee2b synthetic

    model [Figure 2]. The migration result [Figure 2A] shows

    uneven illumination from left sedimentary to subsalt area,

    including shadow zones related to the complex salt

    structures. LS-WEM improves the illumination by

    balancing the image amplitudes and reducing the effects of

    the shadow zones [Figure 2B]. LS-WEM also enhances

    temporal resolution by broadening the frequency spectrum

    [Figure 2E]. Figure 2C and 2D show that LS-WEM

    balances the wavenumber content and improves the image

    of the faults and dipping salt flacks (indicated by arrows).

    Figure 1: An iterative LSM algorithm solves for the earth

    reflectivity m. It simulates synthetic data dmod by using a

    Born modeling operator, and iteratively update the

    reflectivity image m using migration of the data residual

    ||dobs - dmod||.

    In addition, LS-WEM converges rapidly to the true

    solution, reducing the data residuals by 90% in only four

    iterations [Figure 2F].

    Figure 2: Sigsbee2b 2D synthetic example: (A) WEM image; (B) LS-WEM image; (C) F-K spectrum of WEM; (D) F-K spectrum

    of LS-WEM; (E) Frequency spectra of WEM [red] and LS-WEM [blue]; (F) LS-WEM objective function convergence rate.

    WEM

    (A)

    Least-Squares WEM

    (B)

    2017 SEG SEG International Exposition and 87th Annual Meeting

    Page 4423

    Dow

    nloa

    ded

    09/1

    5/17

    to 2

    17.1

    44.2

    43.1

    00. R

    edis

    trib

    utio

    n su

    bjec

    t to

    SEG

    lice

    nse

    or c

    opyr

    ight

    ; see

    Ter

    ms

    of U

    se a

    t http

    ://lib

    rary

    .seg

    .org

    /

  • Broadband Least-Squares Wave-Equation Migration

    Figure 3: Gulf of Mexico 3D WAZ field data example: (A) Depth slice at 1150m from WEM; (B) Depth slice at 1150m from LS-

    WEM; (C) WEM F-K spectrum; (D) LS-WEM F-K spectrum; (E) Frequency spectra of WEM and LS-WEM.

    Figure 4: Gulf of Mexico 3D WAZ field data example: Inline and xline images from (A) WEM and (B) LS-WEM.

    9000m 15 km

    0

    (A) (B)

    WEM Least-Squares WEM

    2017 SEG SEG International Exposition and 87th Annual Meeting

    Page 4424

    Dow

    nloa

    ded

    09/1

    5/17

    to 2

    17.1

    44.2

    43.1

    00. R

    edis

    trib

    utio

    n su

    bjec

    t to

    SEG

    lice

    nse

    or c

    opyr

    ight

    ; see

    Ter

    ms

    of U

    se a

    t http

    ://lib

    rary

    .seg

    .org

    /

  • Broadband Least-Squares Wave-Equation Migration

    We also applied the LS-WEM to a wide azimuth (WAZ)

    data from the Gulf of Mexico. The results also demonstrate

    that LS-WEM can deliver superior images compared to the

    standard migration [Figure 3 and 4].

    Figure 5: North Sea 3D NAZ field data example. Top:

    WEM results; Bottom: LS-WEM results. The depth slice is

    at 1.8km.

    The image improvements of LS-WEM over the standard

    migration can be summarized as: reduction of sail line

    acquisition footprint (lateral stripes indicated by arrows in

    Figure 3A), better resolution, and improved wavenumber

    content [Figure 3C, 3D and 3E]. The inline images also